The present invention relates generally to signal processing systems, and more particularly to processing the step-like output signals generated by non-ideal, nominally single-pole (xe2x80x9cN-1Pxe2x80x9d) devices responding to possibly time-varying, pulse-like input signals of finite duration, wherein the goal is to recover the integrated areas of the input signals.
The specific embodiments described relate to processing step-like signals generated by detector systems in response to absorbed radiation or particles and, more particularly, to digitally processing such step-like signals in high resolution, high rate gamma ray (xcex3-ray) spectrometers with resistive feedback preamplifiers connected to large volume germanium detectors. The application of measuring the step-like output signals from xcex3-ray detector preamplifiers to measure the xcex3-rays"" energies is just a specific example, and is described because this was the area in which the method was first developed.
The techniques that we have developed solve this problem generally, and therefore should not be construed as being limited to this specific application. Any detection system, for example, that produces output current signals that are integrated by charge sensitive preamplifiers could be treated by these techniques, whether the detected quantities are light pulses, x-rays, nuclear particles, chemical reactions, or otherwise. The techniques, in fact, is not limited to xe2x80x9cdetector systemsxe2x80x9d per se, but are, in fact, general purpose signal processing techniques which may be broadly applied, once understood. The outputs from superconducting bolometers, for example, produce step-like signals that are readily treated by the invention. The field of gamma spectroscopy, where 0.1% or less makes the difference between a bad and a good detector, however, provides particularly stringent tests of our techniques.
The term xe2x80x9cstep-like signalxe2x80x9d also requires some discussion. The output of an ideal single-pole (xe2x80x9c1Pxe2x80x9d) device to an ideal impulse (delta) function input, is an infinitely fast rise time followed by an exponential decay whose time constant xcfx84d is characteristic of the pole. Viewed on a time scale short compared to xcfx84d, this output will look like a pure step, while, when viewed on a time scale long compared to xcfx84d, it will look like a pulse. A real 1P device output, however, will have a finite risetime, xcfx84r, whose duration will be determined both by the nature of the device and, particularly, by the duration of its real input signal. Provided that xcfx84r is significantly shorter than xcfx84d, a real 1P device output signal, viewed on a time scale comparable to xcfx84d, will then show a risetime region, whose shape may be difficult to describe mathematically, followed, after a period comparable to xcfx84r, by an exponential decay with time constant xcfx84d. The output of a N-1P device will be similar, with additional distortions. We will refer to such signals, viewed on this time scale, as xe2x80x9cstep-likexe2x80x9d.
The detection and measurement of xcex3-ray energies is a well-established discipline whose primary goal is to accurately determine both the number and energies of xcex3-rays emitted from some target source. The requirements of good energy resolution and high count rate capability usually conflict, however, since count rates are enhanced by increasing detector volume, which increases output signal distortion and so degrades energy resolution. High count rates also degrade energy resolution directly due to practical problems in preamplifier design.
The field of xcex3-ray detection is highly developed. A fairly comprehensive introduction to the state of the art may be found in the volume xe2x80x9cRadiation Detection and Measurement, 2nd Ed.xe2x80x9d by Glenn F. Knoll [KNOLL-1989]. Below we note only the issues relevant to the present invention. In the first section, we discuss how pole/zero cancellation errors introduce a second pole, spoiling the preamplifier""s single pole response. In the second section, we examine how the finite input signal duration, in this case due to charge collection, distorts the preamplifier""s output from the ideal.
FIG. 1A shows a typical solid state xcex3-ray spectrometer comprising a semiconductor detector diode 7 biased by a voltage supply 8 and connected to a preamplifier 10 comprising an amplifier 13 with a feedback capacitor C 15 and resistor R 17. As drawn, preamplifier 10 is a single pole circuit whose response to an impulse (delta function) input is A exp(xe2x88x92t/xcfx842), where xcfx842=RC and A is the area under the impulse. Because xcfx842 is typically of order 1 ms, which is too long for the following circuits, a pole/zero (P/Z) network 20 cancels the pole at 1/xcfx842 and replaces it with a pole at 1/xcfx841, where xcfx841 typically is 50 xcexcs. Gain stage 22 then amplifies and buffers the preamplifier""s output signal for shaping amplifier 23 which feeds multichannel analyzer (MCA) 24.
If the time duration of the current pulse arising from the charge deposited in detector 7 by a xcex3-ray absorption is very short compared to xcfx841, the output of stage 22 will be an exponentially decaying step whose amplitude is the pulse integral and proportional to the deposited charge. xcex3-ray spectrometers are therefore designed to measure these step amplitudes to measure the charge deposited by the absorbed xcex3-ray. Other forms of radiation, including neutrons, alpha and beta particles, and x-rays behave similarly and their energies are measured the same way.
Commonly, however, both the input""s finite duration and the pole-zero circuit""s imperfections distort the preamplifier""s response, destroying the proportionality between the output step""s amplitude and the deposited charge and so degrading the system""s energy resolution. Imperfections in P/Z network 20 arise from difficulties in precisely canceling the xcfx842 component, leaving a small residual fraction, of order 1-2%, in the output signal. FIG. 1B shows a 5% residual xcfx842 component for ease of viewing: an exponential decay signal 25 with time constant xcfx842, input to the P/Z network 20, produces either output signal 27 or 29, depending upon whether the residual xcfx842 term is positive or negative.
These xcfx842 residuals are particularly bothersome at high counting rates, where each signal step rides upon a xcfx842 background from all preceding steps. As these arrive randomly, the resulting baseline bias also fluctuates randomly in time, which the spectroscopy amplifier""s baseline restoration circuit cannot track well. These terms, which may only be a few tenths of 1%, become a significant resolution degradation at 1 MeV where 0.05% energy resolution is desired.
FIG. 2 shows a preamplifier 10 front end with a cross sectional view of the detector 7 of FIG. 1, for the common coaxial geometry, The dashed lines show electric field line within the detector body 30, which vary considerably with local geometry. Two factors cause charge collection time variations within the detector and thus risetime variations in the preamplifier""s 10 signal output: 1) the difference between carrier velocities; and 2) the existence of different path lengths within the detector. RAUDORPH-1982 describes these issues. These risetime variations produce ballistic deficit by two paths, one direct, one indirect. The direct effect is well understood, per GOULDING-1988: the output filter""s response varies with the time dependent shape of the charge arrival, being the convolution of the two. A trapezoidal filter greatly reduces this effect in the absence of exponential decay.
The indirect effect source of ballistic deficit is due to fluctuations in charge loss through the feedback resistor with differing risetime, as seen in FIG. 3A with two risetimes, 40 and 42, where FIG. 3B enlarges their peak regions. The slower risetime signal loses less charge and thus is larger once charge collection is complete. Even filters which ignore the charge collection region are still sensitive to this lost charge effect, and relatively small errors of this size can substantially degrade resolution. For a trapezoidal filter, the collection time difference shown FIG. 3B produces a 0.2% amplitude difference (2,000 eV at 1 MeV) which will degrade ideal 1.7 keV resolution to 2.6 keV. Ballistic deficit errors must therefore be reduced to less than 0.05% to obtain ideal spectrometer resolutions at 1 MeV.
Charge trapping also produces errors in xcex3-ray energy measurements since trapped charges are lost to the measurement. The present invention does not seek to address this problem.
It is important to note that the pole-zero cancellation errors described above do not arise from the preamplifier""s use in xcex3-ray spectroscopy, but are a generic problem in low noise, charge sensitive preamplifiers. Similarly, while the described risetime fluctuations described above were attributed to the geometry and construction of large volume Ge detectors, it is clear that such problems fundamentally arise from interactions between the finite charge collection time and the electrical characteristics of the preamplifier and not from the physics of the collection processes. Geometric heat flow variations in the photon absorbing mass produce similar effects in the superconducting bolometers mentioned earlier. Risetime issues are therefore a potentially general problem as well, and may need to be corrected for in other, non-xcex3-ray, detectors whenever the highest measurement accuracies are required. The methods we describe offer just that capability. Further, the terminology xe2x80x9csingle-polexe2x80x9d or xe2x80x9cmultiple-polexe2x80x9d comes from the LaPlace Transform treatment of differential equations describing time variant phenomena. Any device which shows xe2x80x9csingle polexe2x80x9d behavior, for example, will display exponential time decay in response to an impulse input and, therefore, may be, for example, mechanical, thermal, chemical, or magnetic in nature in addition to the electronic case presented here. Our method can be directly applied to these devices as well, as will be apparent from the teachings herein.
The prior art deals with pole/zero errors in two ways: first, by canceling xcfx842 as accurately as possible; and, second, with baseline restoration schemes which try to track the shaping amplifier""s xe2x80x9cno signalxe2x80x9d output as closely as possible, an approach which degrades as rates becomes high. We have not found any approaches which measure and/or correct for the effect directly.
Over the years, various heuristic schemes have been developed which attempt to compensate for ballistic deficit. RADEKA-1982 introduced trapezoidal filtering and developed a time-variant implementation, using a gated filter following a semi-Gaussian shaper, that provided significant resolution improvements. WHITE-1988 proposed a different gated integration approach using a series switch to excise the charge collection region out of the preamplifier signal entirely. The final circuit was complex and had enhanced deadtime problems. GOULDING-1988, RAUDORF-1982, and SIMPSON-1990 disclose schemes that depend on directly measuring the signal""s risetime tr and correcting the energy filter output by a term like trn. These approaches are complex to implement and require precise expert adjustments to operate. The underlying assumptions are not particularly valid and improvements in energy resolution have been modest in practice.
HINSHAW-1991 and KUMAZAWA-1998 describe attempts to correct for ballistic deficit by capturing peak amplitudes from two filters which respond to the ballistic deficit differently, one an energy measuring filter and one a differentiating (or bipolar shaping) filter. Typically a significant fraction of their difference in peak heights is added to the energy filter""s peak to correct it.
There is some related art wherein the details of the shapes of the preamplifier output signals are sampled digitally and used either to distinguish between different types of particles absorbed in the detector (e.g., MILLER-1994) or to distinguish between single and multiple interaction events in large germanium detectors. See, for example, TAKAHASHI-1994 and AALSETH-1998.
WARBURTON-1997, WARBURTON-1998, and WARBURTON-1999 describe methods for implementing digital filtering and x-ray spectroscopy. While they do not address the issues under consideration, some of their filtering techniques will be employed in the present invention and are referenced in the specification.
The present invention provides techniques for measuring a step-like output signal from a nominally single-pole (N-1P) device in response to a pulse-like input signal to determine the integrated area of said input signal. The invention addresses the possibility that the device deviates from ideality due to the presence of additional poles, zeros and/or a DC offset and that the input pulses may have finite time durations and variable amplitudes. In a specific example, the measurement determines collected detector charges from step-like preamplifier output signals in the presence of both risetime fluctuations and imprecise pole/zero cancellations.
In brief, the present invention contemplates processing the N-1P device""s (e.g., preamplifier""s) output signal using a set of one or more shaping filters. Where plural filters are used, they typically have different time constants. A set of samples of the outputs of this filter set is captured in such a manner that the multiple sample values bear prescribed time relationships to one other. We refer to this set of sample values as a correlated multiple output sample (or xe2x80x9ccMOSxe2x80x9d for short). The relationships among the individual sample values may be determined by the times of their capture, by delay elements inserted in the signal paths, or some combination of the two. Further, the different individual sample values can be obtained from associated different filters, or plural sample values can be obtained from the same filter, but captured at different times or with different delays. The term cMOS is intended to cover these multiple possibilities and is discussed further in xc2xa7 5.1 below.
The input pulse""s integrated area is determined by capturing a cMOS in response to detecting a step-like signal (sometimes called an event). A weighted sum of the individual sample values in the cMOS (sometimes referred to as cMOS values) is then formed as a measure of the input pulse""s integrated area (e.g., total charge). The weighting factors can be computed directly from information about the N-1P device""s decay constants, the filter set, and the prescribed time intervals in the cMOS.
While embodiments of the invention use triangular and trapezoidal filters, the invention does not require specific filter shapes. Further, the invention does not require that the filter""s capture times be precisely located relative to the step-like signal""s leading edge. Rather, the method derives its accuracy from repeatably reproducing the set of prescribed time relationships between the sample values in the cMOS. The underlying capture method is therefore time-based rather than amplitude-based, which differentiates the invention from prior art methods which capture filter samples based on their maximum amplitudes.
While the preferred implementation uses digital signal processing, implementations using solely analog processing or hybrid approaches are also feasible. Embodiments of the invention require neither a measurement of the step-like signal""s risetime nor more precise information about its arrival time than is found by the pileup inspection circuits of commonly available commercial shaping amplifiers.
When using a single cMOS, however, the measurement""s noise is increased by the number N of additional filter samples required to compensate for the N-1P device""s non-ideal terms. For those cases where this increased noise is significant, we also show how N may be reduced by creating a parameterized model of the non-ideal terms; making baseline measurements to determine the parameters; and then using them to correct area (e.g., charge) measurements made using simpler sets of filters which have less noise. In some implementations, these baseline measurements are cMOS values captured at times when the filters are not processing the step-like signals. In the detector-preamplifier case described in detail, the resultant implementation achieves the low electronic noise levels of conventional trapezoidal filters while also eliminating resolution loss due to both ballistic deficit and high count rates.